Axion-like particles could be hypothetically produced in the early Universe by non-thermal mechanisms, such as “vacuum misalignment" [1]}. Then, they form a coherently oscillating classical field \(a(t)=a_{0}\cos (2\pi \nu _{a} t)\)  [2]}. The axion-like dark matter field \(a(t)\)  oscillates at its Compton frequency
\(\begin{aligned}&\nu _{a}=\dfrac{m_{a}c^{2}}{h},\end{aligned}\) 
